The present invention relates generally to investigating earth formations traversed by a borehole. More particularly, the invention relates to methods for determining the permeability of an earth formation traversed by a borehole from well logging data derived by lowering in the borehole one or more apparatus for investigating subsurface earth formations.
Because the permeability of a hydrocarbon bearing formation is a prime indicator as to whether the hydrocarbons may be produced, the oil industry has long been interested in developing a reliable and accurate permeability log. Over the years, a large number of permeability "transforms" have been developed which relate permeability to at least one other aspect of the earth formation. Thus, for example, it is sometimes found in certain formations that a correlation exists between the porosity of the formation and the logarithm of permeability of the formation according to the following relationship: EQU log k-log B.sub.2 =-B.sub.1 .phi. (1)
where k is the formation permeability, .phi. is the formation porosity, and B.sub.1 and B.sub.2 are empirical constants. If equation (1) was accurate and reliable, permeability could be determined on a continuous basis from logging tools as many different tools for and manners of deriving a porosity determination are known in the art. However, typically, the correlation provided by equation (1) is poor and not transferrable from zone to zone or oil field to oil field.
Other transforms which relate permeability to other formation parameters have also been proposed and are currently in use. Thus, A. Timur suggests in "An Investigation of Permeability, Porosity, and Residual Water Saturation Relationships", Proceeding of 9th Ann. SPWLA Logging Symp. June 23-26, 1968, Paper J, that an improved permeability estimate might be derived from a determination of porosity and residual water saturation according to the equation: ##EQU1## where k is the formation permeability, .phi. is the formation porosity, and S.sub.wr is the residual water saturation of the formation. While the standard error of the permeability estimate provided by equation (2) is only a factor of two (which is considered very good for this art), a determination of residual water saturation can only be made in the lab. Thus, borehole sampling techniques (e.g. coring) which are extremely costly and require extensive time delays would be required to use equation (2), and permeability from logging would not be realized. While the residual water saturation determination can be replaced by determinations derived from the free fluid index of the formation, the standard error rises precipitously. Thus, if nuclear magnetic resonance is used downhole to determine the free fluid index as is suggested by A. Timur, "Effective Porosity and Permeability of Sandstones Investigated Through Nuclear Magnetic Resonance Principles", Proceedings of 9th Ann. SPWLA Logging Symp., June 23-26, 1968, Paper K, the standard error increases to a factor of between ten and twenty. Such an error factor, while competitive with other techniques available, is unacceptable in many situations.
Yet another permeability transform, known in the art as the Kozeny-Carman relationship, relates the permeability of a porous medium to the porosity and the surface area per unit volume of the solid matrix according to the equation: ##EQU2## where k is the formation permeability, .phi. is the formation porosity, and S.sub.o is the surface area per unit volume of the solid formation matrix. Other forms of equation (3) exist which normalize the surface area to bulk volume and to pore volume. Nonetheless, all known forms of the equation still require borehole sampling techniques, and the expression is not measurable by borehole logging.
It is therefore an object of the invention to provide a reliable and accurate technique for determining the permeability of an earth formation through the use of logging tools.
It is a further object of the invention to provide reliable and accurate permeability determinations in an earth formation by using logging techniques to provide mineralogical information and porosity indications.